A new car sells for $30,000. The value of the car decreases by 16% annually. How much is the car worth after 10 years? Show all steps and identify the variables.

The car would be worth $5247 after 10 years.

Step-by-step explanation:

The rate at which the value of the car is deprecating is exponential. We would apply the formula for exponential decay which is expressed as

A = P(1 - r)^t

Where

A represents the value of the after t years.

t represents the number of years.

P represents the initial value of the car.

r represents rate of decay.

From the information given,

P = $30,000

r = 16% = 16/100 = 0.16

t = 10 years

Therefore

A = 30000(1 - 0.16)^10

A = 30000(0.84)^10

A = $5247

$5247

Step-by-step explanation:

Reduced by 16% means it's 84% of the previous year

30000×(0.84^10)

= $5,247.0368629794

where is the figure